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Mean-value theorem for the modulus of multiple trigonometric sums

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Abstract

A two-dimensional analog of the Vinogradov mean-value theorem for the modulus of trigonometric sums is proven.

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Literature cited

  1. I. M. Vinogradov, Method of Trigonometric Sums in Number Theory [in Russian], Moscow (1971).

  2. I. M. Vinogradov, Selected Works [in Russian], Moscow (1952).

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  5. A. A. Karatsuba, “Mean-value theorem and complete trigonometric sums,” Izv. Akad. Nauk SSSR, Ser. Mat.,30, 183 (1966).

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  6. A. A. Karatsuba, “Mean value of the modulus of a trigonometric sum,” Izv. Akad. Nauk SSSR, Ser. Mat.,37, 1203 (1973).

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Authors and Affiliations

  1. V. A. Steklov Mathematics Institute, Academy of Sciences of the USSR, USSR

    G. I. Arkhipov

Authors
  1. G. I. Arkhipov
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Additional information

Translated from Matematicheskie Zametki, Vol. 17, No. 1, pp. 143–153, January, 1975.

The author expresses his gratitude fo Prof. A. A. Karatsuba for guidance and Prof. S. B. Stechkin for careful consideration of the paper and useful advice.

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Arkhipov, G.I. Mean-value theorem for the modulus of multiple trigonometric sums. Mathematical Notes of the Academy of Sciences of the USSR 17, 84–90 (1975). https://doi.org/10.1007/BF01093850

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  • DOI: https://doi.org/10.1007/BF01093850

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